Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Relative to origin $O$, the position vectors of points $A$ and $B$ are given by $\vec{OA} = \begin{pmatrix} p \\ 1 \\ 1 \end{pmatrix}$ and $\vec{OB} = \begin{pmatrix} 4 \\ 2 \\ p \end{pmatrix}$, with $p$ taken as a constant.
(i)[3]
If $OAB$ is a straight line, State the value of $p$ and Find the unit vector in the direction of $\vec{OA}$.
(ii)[5]
When $OA$ is perpendicular to $AB$, determine the possible values of $p$.
(iii)[2]
When $p = 3$, $OABC$ is a parallelogram. Find the position vector of $C$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct value is $p = 2$.” …